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Russia Voronezh
Section Mathematics
Title On a generalized boundary value problem for a feedback control system with infinite delay
Author(-s) Afanasova M.S.a, Obukhovskii V.V.a, Petrosyan G.G.b
Affiliations Voronezh State Pedagogical Universitya, Voronezh State University of Engineering Technologiesb
Abstract We consider a non-local boundary value problem for a feedback control system described by a semilinear functional-differential inclusion of fractional order with infinite delay in a separable Banach space. The general principle of existence of solutions to the problem in terms of the difference from zero of the topological degree of the corresponding vector field is given. We prove a concrete example (Theorem 6) of the implementation of this general principle. The existence of an optimal solution to the posed problem is proved, which minimizes the given lower semicontinuous quality functional.
Keywords feedback control system, optimal solution, fractional differential inclusion, infinite delay, measure of noncompactness, condensing operator, fixed point, topological degree
UDC 517.977
MSC 34A08, 34A60, 47H11, 49J53, 49K27
DOI 10.35634/vm210201
Received 25 November 2020
Language Russian
Citation Afanasova M.S., Obukhovskii V.V., Petrosyan G.G. On a generalized boundary value problem for a feedback control system with infinite delay, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 2, pp. 167-185.
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